Scientific Notation and Exponent Rules

Scientific Notation Used to write very large numbers or very small numbers N x 10 n where 1 N < 10 and n is an integer

Standard Notation to Scientific Notation Drop of water contains this many molecules 33,000,000,000,000,000,000 3.3 x 1019 Relative Density of Hydrogen 0.0000899 g/cm3 8.99 x 10-5

3,400 3.4 x 103 0.010 1.0 x 10-2 1,000,000 1 x 106 4.5 4.5 x 100

Product Rule for Exponents Rule #1 - When dividing like bases, subtract the exponents. Rule #2 - When multiplying like bases, add the exponents.

Product Rule for Exponents x2 x3 = x5 xm xn = x m+n 107 102 = 6 x 102 7 x 105 = 25 x 105 2 x 105 = 109 42 x 107 = 4.2 x 108 50 x 1010 = 5.0 x 1011

DD (degree day): degrees over 65 or under 65 in a day. General definitions: BTU (British Thermal Unit): energy it takes to raise 1 pound of water 1 degree F DD (degree day): degrees over 65 or under 65 in a day. Ex. 80 degrees is equal to 15 cooling DD or 55 degrees is equal to 10 heating DD You can count this up for a month or year and get an idea of how much you might spend on your energy bill in that area

Hotchkiss Power Plant, Average Year Oil = 273,704 gallons Electricity = 1,071,312 kwh Space = 348,355 square feet DD = 6870 DD Costs: Oil $22.60 per barrel Electricity 8.5 cents/kwh

Oil 273,704 gallons x 150,000 BTU 1 gallons = 4.11 x 1010 BTU Elec. 1,071,312 kwh x 3413 BTU 1 kwh = 3.66 x 109 BTU Total BTU: 4.11 x 1010 BTU + 0.366 x 1010 BTU = 4.476 x 1010 BTU

Calculating cost Oil 3,914,419 gallons $22.60/barrel Elec. 1,071,312 $0.085/kwh Oil: 273,704 gallons x 1 Barrel x $22.60 = 42 gallons 1 Barrel $147,278.82 Elec.: 1,071,312 kwh x $0.085 = $91,062.52 kwh $147,278.82 + $91,061.52 = $238,341.34